# Homework 5: Heaps

**Due before class on Monday, November 7**

Remember to turn in a neat final draft of this homework on a separate sheet of paper.

- Write down the array that would be used to store the following heap:

- Draw the heap represented by the following array:

`[None, 81, 64, 70, 40, 1, 48, 10, 30]`

- Starting with the following array-based heap, show the resulting array
after performing the following series of insertions. You can show any of your
work, but be sure to
**clearly indicate the array after each insertion**.1 2 3

insert(20) insert(60) insert(85)

`[None, 82, 41, 79, 39, 15, 46, 49, 38]`

- Starting with the following array-based heap, show the resulting
array after performing the following series of removals. You can show
any of your work, but be sure to
**clearly indicate the array after each removal**.1 2 3

removeMax() removeMax() removeMax()

`[None, 93, 63, 87, 50, 61, 78, 35, 38, 40, 6, 26]`

- Show the resulting array-based heap after performing a
**bottom-up heapify**on the following list:

`[None, 31, 7, 56, 52, 98, 18, 56, 5, 40, 86, 85, 31, 83, 14, 46, 95, 20]`